In this paper, a set of Dombi power partitioned Heronian mean operators of q-rung orthopair fuzzy numbers (qROFNs) are presented, and a multiple attribute group decision making (MAGDM) method based on these operators is proposed. First, the operational rules of qROFNs based on the Dombi t-conorm and t-norm are introduced. A q-rung orthopair fuzzy Dombi partitioned Heronian mean (qROFDPHM) operator and its weighted form are then established in accordance with these rules. To reduce the negative effect of unreasonable attribute values on the aggregation results of these operators, a q-rung orthopair fuzzy Dombi power partitioned Heronian mean operator and its weighted form are constructed by combining qROFDPHM operator with the power average operator. A method to solve MAGDM problems based on qROFNs and the constructed operators is designed. Finally, a practical example is described, and experiments and comparisons are performed to demonstrate the feasibility and effectiveness of the proposed method. The demonstration results show that the method is feasible, effective, and flexible; has satisfying expressiveness; and can consider all the interrelationships among different attributes and reduce the negative influence of biased attribute values.

Q‐Rung orthopair fuzzy number (qROFN) is a flexible and superior fuzzy information description tool which can provide stronger expressiveness than intuitionistic fuzzy number and Pythagorean fuzzy number. Muirhead mean (MM) operator and its dual form geometric MM (GMM) operator are two all‐in‐one aggregation operators for capturing the interrelationships of the aggregated arguments because they are applicable in the cases in which all arguments are independent of each other, there are interrelationships between any two arguments, and there are interrelationships among any three or more arguments. Archimedean T‐norm and T‐conorm (ATT) are superior operations that can generate general and versatile operational rules to aggregate arguments. To take advantage of qROFN, MM operator, GMM operator, and ATT in multicriteria group decision making (MCGDM), an Archimedean MM operator, a weighted Archimedean MM operator, an Archimedean GMM operator, and a weighted Archimedean GMM operator for aggregating qROFNs are presented to solve the MCGDM problems based on qROFNs in this paper. The properties of these operators are explored and their specific cases are discussed. On the basis of the presented operators, a method for solving the MCGDM problems based on qROFNs is proposed. The effectiveness of the proposed method is demonstrated via a numerical example, a set of experiments, and qualitative and quantitative comparisons. The demonstration results suggest that the proposed method has satisfying generality and flexibility at aggregating q‐rung orthopair fuzzy information and capturing the interrelationships of criteria and the attitudes of decision makers and is feasible and effective for solving the MCGDM problems based on qROFNs.

Two important tasks in multiattribute group decision-making (MAGDM) are to describe the attribute values and to generate a ranking of all alternatives. A superior tool for the first task is linguistic interval-valued intuitionistic fuzzy number (LIVIFN), and an effective tool for the second task is aggregation operator (AO). To date, nearly ten AOs of LIVIFNs have been presented. Each AO has its own features and can work well in its specific context. But there is not yet an AO of LIVIFNs that can offer desirable generality and flexibility in aggregating attribute values and capturing attribute interrelationships and concurrently reduce the influence of unreasonable attribute values. To this end, a linguistic interval-valued intuitionistic fuzzy Archimedean power Muirhead mean operator and its weighted form, which have such capabilities, are presented in this paper. Firstly, the generalised expressions of the AOs are established by a combination of the Muirhead mean operator and the power average operator under the Archimedean T-norm and T-conorm operations of LIVIFNs. Then the properties of the AOs are explored and proved, their specific expressions are constructed, and the special cases of the specific expressions are discussed. After that, a new method for solving the MAGDM problems based on LIVIFNs is designed on the basis of the weighted AO. Finally, the designed method is illustrated via a practical example, and the presented AOs are evaluated via experiments and comparisons.

Laser powder bed fusion (LPBF) provides a rapid and cost-effective solution for fabricating metallic parts with near full density and high precision, strength, and stiffness directly from metallic powders. In LPBF, process variables are widely recognised as fundamental factors that have important effect on the quality of the built parts. However, activity of designing process variables for LPBF, i.e., process planning for LPBF, still heavily depends on knowledge from domain experts. This necessitates a knowledge base that enables the capture, representation, inference, and reuse of existing knowledge. In this paper, a description logic (DL) based ontology for knowledge representation in process planning for LPBF is presented. Firstly, a set of top-level DL entities and specific DL entities and semantic web rule language (SWRL) rules for part orientation, support generation, model slicing, and path planning are created to construct the ontology. The application of the ontology is then illustrated via process planning on an LPBF part. Finally, the benefits of the ontology are demonstrated through a few examples. The demonstration results show that the ontology has rigorous computer-interpretable semantics, which provides a semantic enrichment model for LPBF process planning knowledge and enables automatic consistency checking of the ontology, knowledge reasoning on the ontology, and semantic query from the ontology. This would lay solid foundation for development of a process planning tool with autonomous decision-making capability.